Biogerontology 4: 31–45, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
31
Research article
Biological evidence for limits to the duration of life
Bruce A. Carnes1,∗ , S. Jay Olshansky2 & Douglas Grahn3
1 Center
on Aging, National Opinion Research Center, University of Chicago, 1155 E. 60th Street, Chicago,
IL 60637, USA; 2 School of Public Health, University of Illinois at Chicago, Chicago, IL 60612, USA;
3 Biosciences Division, Argonne National Laboratory, Argonne, IL 60439, USA; ∗ Author for correspondence
(e-mail: [email protected]; fax: +1-630-922-3952)
Received 17 July 2002; accepted in revised form 11 September 2002
Key words: life expectancy, limits, longevity, mortality
Abstract
Projections of duration of life for humans based on mathematical models have led some researchers to claim that
there is no lower limit to death rates or upper limit to life expectancy, and that a life expectancy of 100 will be
achieved in the 21st century. To assess the biological plausibility of these claims, we examined temporal aspects
of biological phenomena in three mammalian species. Our examination revealed that: (1) physiological declines
associated with reproduction consistently occur at ages that are less than one-third of the median age at death, (2)
physiological parameters associated with aging in humans lose eighty percent of their functional capacity by age
80, and (3) young versus old individuals can be distinguished by the pathologies detected at death. The biological
evidence suggests that organisms operate under warranty periods that limit the duration of life of individuals and
the life expectancy of populations. We use these findings to discuss the issue of limits to the duration of life and
the validity of mathematical models used to forecast human longevity.
Introduction
When the Social Security program in the United
States was created in 1935, the actuaries responsible for assessing the future solvency of the program
were required to make forecasts of the number of
beneficiaries that would draw annual benefits from
the program. Consistent with accepted actuarial
methodology, they devised a mathematical approach
to extrapolate past trends in mortality and life expectancy into the future. The logic and methodology was
simple. If life expectancy at birth increased by two
years in the previous two decades, then the extrapolation model yielded a projected increase in life expectancy of two years in the subsequent two decades.
Throughout most of the 20th century the Social
Security Administration (SSA) consistently underestimated the rise in life expectancy. The past invariably had slower rates of mortality improvement than
the future. As a result, the upper limits to life expect-
ancy projected by the SSA model were often exceeded
within just a few years (Olshansky 1988). In addition, the SSA actuaries believed in a fixed biological
limit to life, a now discredited view that at the time
was supported by a widely accepted prediction that
the rise in life expectancy would soon begin to abate
(Bourgeois-Pichat 1978). In the latter part of the 20th
century, the opposite problem occurred – the SSA
overestimated the rise in life expectancy. This time
the actuaries based their forecasts on a time period
when declines in death rates at middle and older
ages were the most rapid in recorded human history.
Consequently, the observed increases were lower than
the projected ones.
In recent years, the extrapolation model has been
invoked to declare that history will repeat itself and
human life expectancy will continue to rise far into
the future. The latest reincarnations of the extrapolation model use longer time frames to compensate
for fluctuating trends in life expectancy that occur
32
over the short-term (Lee et al. 1992). This long-term
extrapolation model has been used to project that life
expectancy at birth will continue to rise throughout
the 21st century (Vaupel et al. 1986; Wilmoth 1998;
Tuljapurkar et al. 2000). Recently, the historic rise
in human life expectancy was described as one of
the most remarkably regular events ever observed,
and it was predicted that this trend would lead to
a life expectancy at birth of 100 years by the year
2060 (Oeppen et al. 2002). The features shared by
the extrapolation models used to forecast life expectancy are simplicity, proven reliability over the shortterm, and a disregard of the biological evidence that
contradicts their long-term applicability. Long-term
forecasts of life expectancy and survival that are
biologically realistic are essential to government agencies responsible for preserving the financial integrity
of age-based entitlement programs like Social Security
and Medicare.
The biodemography of aging
The morphological, physiological and biochemical
attributes that exist within the current generation of
any organism were fashioned by the blind eye of
evolution from the biological materials that were available in preceding generations. Although this genetic
legacy encompasses an extensive array of biological processes, those necessary for extreme longevity
are not among them. As such, aging and death are
inseparable partners to growth and development. The
biological consequences of aging in the form of fatal
and non-fatal aging-related diseases and disorders are
revealed when individuals manage to live beyond
their reproductive period. For humans and laboratory
animals that are protected from environmental threats,
remarkably predictable age patterns of morbidity and
mortality (Olshansky et al. 1991; Carnes et al. 1996)
suggest that the functional duration of bodies are
constrained by what we will call ‘biological warranty
periods’.1
Explanations for why death occurs and when the
warranty period for living things expires can be found
within the field of evolutionary biology (Williams
1957; Hamilton 1966). Although differing in the
mechanisms involved, a common theme runs through
the evolutionary theories of aging. It begins with the
premise that the hostile environments of the natural
world have always posed an insurmountable barrier
to indefinite survival, making immortality unattain-
able even if organisms possessed a biology capable
of eternal life (Carnes et al. 1993). No organism
escapes death and the vast majority die prematurely
from predation, starvation, and infectious diseases –
causes of death that are largely extrinsic to the biology
of aging (Carnes et al. 1997). Not only would the
energy costs of maintaining the functional integrity
of an organism for an indefinite time be prohibitively expensive (Kirkwood 1977), but a strategy
that diverts physiological resources away from reproduction would be a recipe for certain failure in a
world where extrinsic causes of death (Medawar 1952)
make indefinite survival impossible (Weismann 1891).
Faced with an implacably hostile world, life on earth
discovered an effective strategy for coping with the
inevitability of death. The solution was to make
genes immortal rather than the bodies that carry them
(Dawkins 1976).
We contend that the bodies of organisms are
subject to biological warranty periods, and that the
manifestations of aging are most clearly evident when
the duration of life is extended beyond those warranty
periods. Data on reproduction, physiological function
over time, and the spectrum of pathology observed at
death for three distinct mammalian species (mouse,
dog and human) are used to explore the existence
of biological warranty periods, and to identify their
approximate expiration dates. Finally, limits on the
duration of life of individuals and the life expectancy
of populations, as well as the credibility of mathematical models that predict much higher life expectancies
in the latter part of the 21st century will be discussed
within the context of our biological findings.
Animal data
Duration of life experiments using a wide variety
of laboratory mice (e.g., inbreds, hybrids, backcross
generations) and the beagle dog were conducted over a
40-year period in the Biological and Medical Research
Division at Argonne National Laboratory (ANL) in
order to investigate the biological consequences of
exposure to radiation (Grahn 1994; Grahn et al. 1995).
Data on control animals from the extensive mortality
and pathology databases compiled for these studies
as well as reproductive data from the ANL breeding
colony that produced them were used for all analyses
in this paper involving laboratory animals. Additional
pathology and mortality data for the beagle were
provided by the Lovelace Respiratory Research Insti-
33
tute in Albuquerque, New Mexico – formerly known
as the Inhalation Toxicology Research Institute.
Experimental protocol at ANL required that
animals be allowed to die a natural death (i.e., medical
interventions were not used to extend life). Pathology
judgments were based on histological examinations
performed by certified veterinary pathologists. When
an animal died, a single cause of death was established
(designated ‘L’), pathologies judged to have contributed to death were identified (designated ‘C’), and the
remaining pathologies considered non-contributory
(designated ‘N’) were also recorded. Mouse pathologies were assigned a unique four-letter pathology
code, while the pathological assessment of dogs was
based on codes from the Systematized Nomenclature
of Medicine (SNOMED 1982) and the Systematized Nomenclature of Veterinary Medicine (SNOVET
1984). A translation between mouse and dog coding
was created at ANL. When a cause of death could
not be determined, the examining pathologist assigned
cause of death unknown (CDU) to that animal.
The breeding colony of mice at ANL used single
pair matings. The identity of every Dam and Sire for
22 strains (including inbreds, hybrids and backcross
generations) were known and details of their reproductive history were recorded. Among these details
were litter number (parity), gender and number of
pups born, pup death prior to weaning, and the time
interval (in days) between successive litters.
Human data
We used the most complete source of information
on mortality in the United States – death certificates
compiled by the National Center for Health Statistics (NCHS 1998). This file contains underlying and
contributing causes of death for all recorded decedents
in the United States in 1996. Each death record also
contains information on age, sex, race, and up to
16 multiple causes of death, as well as basic demographic details of the decedents (e.g., marital status,
usual occupation, education). The underlying cause is
selected from an array of conditions reported in the
medical certification section on the death certificate
by the attending physician, and is defined as ‘(a) the
disease or injury which initiated the train of events
leading directly to death, or (b) the circumstances
of the accident or violence which produced the fatal
injury’. These are then translated into standardized
medical codes according to the 9th Revision of the
International Classification of Diseases (ICD 1989).
Because autopsies are rare (Johnson et al. 1998),
the diagnoses reported on death certificates are not
based on thorough pathological examination. We only
considered deaths for individuals over age 20 because
age-related diseases were the focus of our mortality
analyses. We also applied a multiple cause pattern
called the ‘total mentions’ approach which considers
all conditions present on the death certificate, regardless of their relationship with other conditions listed
(Hummer et al. 1998).
Human age-specific fertility rates were taken from
reports produced by the National Center for Health
Statistics (Ventura et al. 1998; NCHS 2002). In most
cases, age of mother was computed from the mother’s
and infant’s dates of birth as reported on the birth
certificate. Information on age of father was also taken
from birth certificates. Births with unknown paternal
age were distributed in the same proportions as births
with known paternal age within each five-year age
classification of mother. Data representing a natural
fertility population (the Hutterites) were taken from
the published literature (Eaton 1953). Age-specific
fertility rates for a high mortality/high fertility human
population were generated as a composite fertility
schedule based on survey data from the following
three countries (equally weighted) – Mali (1987),
Niger (1998), and Uganda (1988) (Demographic and
Health Surveys 2002). These countries were chosen
because all three had total fertility rates (TFR; total
births per woman) in these years that exceeded 7.0.
Single-year-of-age fertility rates for this population
were then generated through a linear interpolation
between the mid-year fertility estimates for the fiveyear age groups.
Methods
For the most frequently used mice in the ANL experiments (five strains: A/Jax, BALB/c, C57BL/6, C57L;
and one hybrid: B6CF1 ) the database for the breeding
colony was used to calculate average values for litter
size, pup mortality in the pre-weaning period, and the
time interval between parities for every Dam (Grahn
1972). These reproductive summary statistics were
plotted as a function of maternal age. For 22 mouse
strains (including those previously mentioned), reproductive data from the breeding colony were used to
estimate an effective end of reproduction (EER) for
each Dam. EER was operationally defined as the
34
maternal age when a Dam’s cumulative lifetime births
reached 75% and pre-weaning pup mortality within a
litter exceeded 35%. An average EER was then calculated for each of the 22 strains. For the control mice
produced from these matings, a Gompertz distribution generalized for competing risks was used in order
to estimate a median age at death (MAD) for causes
of death judged from pathologic examination to have
arisen from genetic and/or degenerative processes.
These MAD values were then used as the dependent
variable in a regression analysis with EER as the sole
predictor variable.
For the investigation of age-dependent change in
the types and frequency of pathology detected at
death (subsequently referred to as pathology shifts),
the pathology codes for the B6CF1 mouse (the most
frequently used mouse, and the one with the most
detailed pathology data) and beagle dog were classified into a number of non-overlapping categories
referred to as combined pathology groups. Two
causes of death (cancer and diseases of the cardiovascular system) were chosen because these two
disease categories also account for the vast majority
of human deaths. Because of their importance, cancer
and cardiovascular disease were further partitioned
into their ‘L’, ‘C’ and ‘N’ subgroups (see Data
description for definitions). For the B6CF1 mouse,
the remaining combined pathology groups were organized around organ systems: liver and biliary tract,
lungs and pleura, reproductive organs and urinary
tract. The greater pathology detail available for the
beagle dog permitted additional groups to be established: digestive system, endocrine, hematopoietic,
skeletal system and skin. Similarly, the death certificate data for humans permitted not only the inclusion
of the pathology groups used for the beagle, but
also categories for diseases of the eye and adnexa,
mental disorders and diseases of the nervous system.
Finally, codes not falling into any of the specific
pathology groups were assigned to a miscellaneous
group referred to as ‘other’. Except for cancer and
cardiovascular diseases, no distinction between L, C
or N was made (i.e., no distinction was made between
lethal, contributory or non-contributory pathologies).
For every animal, the number of pathologies falling
within each of the combined pathology groups was
determined. In other words, the multiple pathology
records that exist for an individual animal were
collapsed into one record per animal containing counts
for each of the pathology categories – subsequently
referred to as counting bins.
Age at death plus the counting bins arising from
the above pathology classifications were used as
explanatory variables in logistic regression analyses
(SAS 1995). In logistic regression, the response variable is dichotomous. For example, in these analyses
the response variable was set to 0 or 1 in order
to indicate group membership (e.g., cause of death
known or unknown). The logistic model then uses the
explanatory variables to predict the probability (pi )
that the response variable for a particular individual
is either 0 or 1:
logit(pi) = log[pi/(1 − pi )] = α +
βi x i
(1)
where α is a constant (like an intercept in ordinary
regression), βi are logistic regression coefficients,
xi are the explanatory variables (i.e., age at death
and the pathology counting bins), pi /(1 − pi ) is
the odds ratio, and log[pi/(1 − pi )] is the log odds
ratio or logit (Kleinbaum 1994). In other words, we
used age at death and the frequency and identity
of pathologies observed at death (i.e., the combined
pathology counting bins) in the logistic model in
order to predict a probability that a particular individual is a member of the population specified by
the binary response variable. All available explanatory
variables were included in the initial model, and a
final model was achieved by the progressive elimination of non-significant predictors of group membership.
Two different logistic regression models were
formulated. In one model the binary response was
a contrast between individuals (performed for both
laboratory animals and humans) that died at older and
younger ages. Young or old was operationally defined
as individuals that died in the first or fourth quartile of
the death distribution respectively. In the other logistic
model, the pathology data for the B6CF1 mouse were
used to compare mice that died of known causes of
death to those where a cause of death could not be
determined. The two logistic models differed slightly
in the way that the pathology counting bins were
used as predictor variables. All of the counting bins
(including the L, C and N distinctions) were used in
the young versus old contrast. The L, C or N designations were never used in the analysis of unknown
causes of death because any pathology with an L or C
designation would, by definition, be a perfect predictor
of whether an animal did or did not have a known
cause of death.
Proportional hazard models (Cox 1972) were also
used to investigate the mortality dynamics of B6CF1
35
mice dying from unknown causes. A proportional
relationship between the hazard function for animals
dying of a known cause, λ0 (t), and animals dying from
an unknown cause, λ(t,I), was assumed:
λ(t, I) = λ0 (t)exp[β ∗ I]
(2)
where β is the regression coefficient, I is a binary
indicator variable (I = 0 or 1) used to distinguish
between animals dying from an identified cause (I
= 0) and those where a cause of death could not
be determined (I = 1), and exp[β∗I] is the relative
risk. This model parameterization generates a test
formally identical to the Kaplan–Meier test traditionally used to evaluate the equality of cumulative
survivorship curves. A more detailed inspection of
mortality dynamics was achieved by partitioning the
distribution of failure times (all deaths) into quartiles.
The previously described hazard model was then
applied within each quartile. Deaths falling outside
the quartile being analyzed were considered censored
observations (i.e., contributing to mouse days at risk,
but not counted as events). This modeling approach is
equivalent to taking the Kaplan–Meier homogeneity
chi-square statistic for the entire age spectrum and
dividing it into four additive pieces (Kalbfleisch et al.
1980) – one for each quartile. In other words, age
patterns of mortality for known and unknown causes
of death were compared conditional upon having
survived to and died within a specified quartile of the
cumulative survivorship distribution for all causes of
death. Males and females were analyzed separately.
Results
Reproductive biology
Measures of reproductive performance are plotted
(Figures 1–3) for the five mouse strains (A/Jax,
BALB/c, C57BL/6, C57L) and hybrid (BCF1 ) most
frequently used in the ANL studies. Although variation in reproduction among mouse strains exists, the
biological consequences of increasing maternal age
are evident. Mean litter size decreases (Figure 1),
pre-weaning pup mortality increases (Figure 2), and
the time interval between parities lengthens (Figure
3). Further, these signs of physiological decline
are consistently occurring at ages that are approximately 1/3 of the MAD for these mouse strains. The
trend line (linear regression) in Figure 4 shows that
MAD increased for mouse strains whose mothers
Figure 1. Mean litter size at birth plotted as a function of maternal
age for four mouse strains (A/Jax, BALB/c, C57BL/6, C57L) and
the hybrid (BCF1 ) arising from a cross of the BALB/c and C57BL/6
strains (see Grahn (1972, 1994) for more details).
were capable of reproducing effectively at older ages
(EER). This linkage between longevity and reproduction observed in mice is consistent with research
findings for humans (Holliday 1996; Perls et al. 1997).
Figure 5 presents age-specific cumulative fertility
for human females and males. The fertility data
for females come from a developed country (United
States), a natural fertility population (Hutterites), and
a high mortality/high fertility population (a composite
of women from Mali, Niger and Uganda). Cumulative
fertility for males is depicted only for the male population of the United States in 1996. These data illustrate
a consistent age pattern of reproduction that appears
almost entirely uninfluenced by socioeconomic status,
vast differences in mortality, and variation in the availability and use of contraception. In two of the three
populations, children have been born to females as
young as 10 years of age. Young births either do not
occur or are not reported in the Hutterite population
because marriage is not permitted until age 18. The
figure demonstrates that approximately 75% of the
cumulative reproductive output in these populations
36
Figure 2. Mortality in pups prior to weaning (expressed as a percent
of live births) plotted as a function of maternal age for four mouse
strains (A/Jax, BALB/c, C57BL/6, C57L) and the hybrid (BCF1 )
arising from a cross of the BALB/c and C57BL/6 strains (see Grahn
(1972, 1994) for more details).
is accomplished by the age of 35 for both males and
females.
The regression equation that was used to predict
the median age of intrinsic death of offspring from
their mother’s age at the effective end of reproduction for 22 strains of mice is provided in the header
of Table 1 and illustrated in Figure 4. This equation,
estimated from data for mice, was then used to predict
MAD values for humans. In order to be consistent
with the definition used for mice, the EER values used
to represent humans (ages ranging from 32 to 38) in
the mouse model were selected from the cumulative
fertility plots for humans (Figure 5) evaluated at 75%.
Using these values, the mouse model predicted that the
median age of intrinsic mortality for humans (males
and females combined) should fall between the ages
of 82 and 97 years (Table 1).
Pathology
A comparison of pathology profiles between young
and old B6CF1 mice is summarized in Table 2. Young
mice were defined as those dying within the first
quartile of the failure distribution (before 844 days
Figure 3. The interval width (in days) between successive parities
plotted as a function of maternal age for four mouse strains (A/Jax,
BALB/c, C57BL/6, C57L) and the hybrid (BCF1 ) arising from a
cross of the BALB/c and C57BL/6 strains (see Grahn (1972, 1994)
for more details).
Figure 4. The linear regression and observed data points for the
Gompertz estimated median age at death (MAD for intrinsic causes)
for 22 mouse strains (i.e., inbreds, hybrids and backcross generations) plotted as a function of the age (EER, in days) when
the females that gave birth to those animals were no longer
capable of effective reproduction (i.e., cumulative births >75% and
pre-weaning pup mortality >35%; see Grahn (1972) and Carnes et
al. (1996) for more details).
for females and 854 days for males) while old mice
were defined as individuals surviving into the fourth
quartile of the failure distribution (beyond 1,103 days
for females and 1,123 days for males). Old animals
of either sex died with a significantly elevated tumor
burden as well as an increased number of patholo-
37
Figure 5. Age-specific fertility rates for US males (1996), and females for a low mortality/low fertility population (US, 1997), a natural fertility
population (Hutterites) and a high mortality/high fertility population (a composite of Mali 1987; Niger 1998; Uganda 1988) plotted as a function
of age (in years).
Table 1. Regression of median age at death for intrinsic causes
of death (MAD) on effective end of reproduction (EER) estimated from mouse data and applied to hypothetical human
data.
Human
EER
(years)
Human
EER
(days)
Human
MAD
(years)
32
34
36
38
11680
12410
13140
13870
81.8
86.9
92.0
97.0
MAD = 195 + 2.54 EER; R2 = 0.44.
gies associated with the cardiovascular, lung and
pleura, and reproductive organs. This interpretation
changes little when the predictor variables for cancer
and cardiovascular disease are split into their lethal
(L), contributory (C) and nonlethal (N) subcategories.
With the one exception of lethal tumors in males,
all categories of cancer involvement were elevated
in animals that died at old ages. This more detailed
pathology diagnosis also reveals that the greater
burden of cardiovascular disease in older animals of
either sex is driven by conditions that contributed to
death but were not the primary cause of death.
The results of an identical logistic regression
analysis applied to the pathology data for beagle dogs
are summarized in Table 3. In beagles, the first (before
4,093 days for females and 4,406 days for males)
and fourth (5,385 days for females and 5,565 days
for males) quartiles of the all-cause failure distribution were once again used as an operational definition
of whether animals died at either young or old ages.
Unlike the B6CF1 mouse, only tumors judged to have
neither killed nor contributed to death were elevated
in dogs dying at older ages. Cardiovascular disease
also had no discriminatory power in the dog analysis.
The only pathology other than incidental tumors that
was elevated in old dogs was diseases of the skeletal
system. Endocrine, pulmonary and skin diseases were
also significant predictors of when dogs died, but
these pathologies were elevated in animals that died
at young ages rather than at older ages.
The logistic regression results for human
pathology are summarized in Table 4. In humans,
death at younger ages was defined as occurring
between 20 and 50 years of age, while death beyond
age 80 was considered to have occurred at older
38
Table 2. Summary of odds ratios and their (P-values) generated from logistic regression analyses used to contrast deaths in
the first (young) and fourth (old) quartile of the failure distribution for B6CF1 mice. Odds ratios greater than one indicate
elevated pathologies in old animals. P-values = (0.00) represent significance values less than (0.001). L = cause of death, C
= contributing to death and N = observed at death. NA means variable not included in final model.
Sex
Cancer
L
C
N
Cardio
L
C
4.03 (0.00)
2.85 (0.00)
2.72 (0.00)
2.59 (0.00)
NA
NA
2.29 (0.00)
2.55 (0.00)
2.52 (0.00)
NA
F
M
N
Pul
Repro
1.50 (0.01)
1.74 (0.00)
NA
2.21 (0.00)
2.20 (0.00)
2.01 (0.00)
2.07 (0.00)
2.28 (0.00)
2.29 (0.00)
NA
2.45 (0.00)
2.36 (0.00)
5.86 (0.03)
NA
Cancer: diseases involving cancer.
Cardio: diseases of the cardiovascular system.
Pul: diseases of the respiratory system (lungs and pleura).
Repro: diseases of the reproductive organs.
Table 3. Summary of odds ratios and their (P-values) generated from logistic regression analyses used to contrast deaths in
the first (young) and fourth (old) quartile of the failure distribution distribution for the beagle dog. Odds ratios greater than
one indicate elevated pathologies in old animals. P-values = (0.00) represent significance values less than (0.001). L = cause
of death, C = contributing to death and N = observed at death. NA means variable not included in final model.
Sex
Cancer
L
C
N
Endo
Pul
Skel
Skin
F
M
Both
0.23 (0.01)
NA
0.33 (0.00)
NA
NA
NA
1.37 (0.01)
2.22 (0.00)
1.54 (0.00)
NA
0.65 (0.12)
NA
NA
0.42 (0.01)
0.62 (0.01)
2.58 (0.02)
2.07 (0.07)
2.21 (0.00)
0.36 (0.01)
NA
0.51 (0.01)
Cancer: diseases involving cancer.
Endo: diseases of the endocrine system.
Pul: diseases of the respiratory system.
Skel: diseases of the musculoskeletal system and connective tissue.
Skin: diseases of the skin and subcutaneous tissue.
ages. The striking feature of the analyses of human
pathology observed at death is the number of
significant disease categories. Every disease category
examined, other than the liver, exhibited pathology
burdens in both males and females that were elevated
in individuals dying at older ages. In addition, notable
gender differences were observed for cardiovascular
diseases, mental disorders, and diseases of the
reproductive system.
Table 5 contains a summary of the proportional hazard model analyses used to make mortality
contrasts between B6CF1 mice dying of known causes
versus those where a cause of death could not be
determined. The a priori hypothesis was that animals
dying at older ages have so many things going wrong
with them (i.e., generalized organ failure) that it
becomes extremely difficult to identify a specific cause
of death. If true, then mice classified as having
died of cause of death unknown (CDU) should tend
to die at older ages than mice with an identifiable
cause of death. Although the results of the mortality
analyses were consistent with this hypothesis, the
reality was more complicated. Mortality comparisons made within quartiles of the failure distribution
revealed that mice diagnosed with CDU in the first
quartile died earlier (i.e., relative risk greater than one)
than non-CDU animals. However, once mice survive
beyond the first quartile (approximately 850 days),
the CDU animals died at significantly older ages than
those dying of known causes (i.e., relative risk less
than one).
The logistic regression results summarized in
Table 6 provide additional support for the hypothesis
that CDU animals have a more complex pathology
profile than mice dying of known causes. Although
mice with CDU listed as a cause of death had a higher
overall burden of pathology at the time of death, the
logistic regression analysis revealed that this elevated
39
Table 4. Summary of odds ratios and their (P-values) generated from logistic regression analyses of human data (intrinsic
mortality) used to contrast the pathology burden at younger ages (20–50 years) to that observed at older ages (over 80
years). Odds ratios greater than one indicate elevated pathologies in older humans. P-values = (0.00) represent significance
values less than (0.001).
Sex
Cancer
Cardio
Dig
Endo
Eye
Hema
Kidur
F
M
1.52 (0.00)
1.78 (0.00)
4.26 (0.00)
2.00 (0.00)
2.76 (0.00)
1.47 (0.00)
1.11 (0.00)
0.83 (0.00)
2.39 (0.00)
1.42 (0.01)
1.28 (0.00)
1.29 (0.00)
1.66 (0.00)
1.86 (0.00)
Sex
Lvr
Ment
Neur
Pul
Repro
Skel
Skin
F
M
0.19 (0.00)
0.22 (0.00)
9.52 (0.00)
2.16 (0.00)
2.39 (0.00)
1.53 (0.00)
2.85 (0.00)
3.40 (0.00)
0.82 (0.09)
12.23 (0.01)
1.48 (0.00)
1.69 (0.00)
3.14 (0.00)
2.11 (0.00)
Cancer: diseases involving cancer (ICD 140-239).
Cardio: diseases of the circulatory system (ICD 390-459).
Dig: diseases of the digestive system (ICD 520-579).
Endo: endocrine, nutritional, and metabolic diseases and immunity disorders (ICD 240-279).
Eye: disorders of the eye and adnexa (ICD 360-379).
Hema: diseases of blood and blood-forming organs (ICD 280-289).
Kidur: diseases of urinary tract (ICD 580-599).
Lvr: diseases of liver and biliary tract (ICD 571-575).
Ment: mental disorders (ICD 290-319).
Neur: diseases of the nervous system other than sense organs (ICD 320-359).
Pul: diseases of the respiratory system (ICD 460-519).
Repro: diseases of the reproductive organs (ICD 600-629).
Skel: diseases of the musculoskeletal system and connective tissue (710-739).
Skin: diseases of the skin and subcutaneous tissue (ICD 680-709).
burden could not be linked to any specific organ
system – a finding consistent with generalized organ
failure (i.e., multiple pathologies distributed across
multiple organ systems).
Physiological parameters
The physiological changes that occur in humans
with the passage of time have been documented in
the scientific literature and known for decades (e.g.,
Falzone et al. 1956; Shock 1957; Norris et al. 1956).
Some of these changes are described in a seminal
article published in 1960 and still frequently cited
(Strehler 1960) in which the percentage of reserve
capacity remaining for various organ systems was
estimated for humans between the ages of 20 and
90. Reserve capacity or vitality was described as
a quantifiable age-dependent change in functioning
between the maximum levels observed at birth and
a lower limit of functioning that was defined by the
lowest measured individual value, by organ system,
for a population. Average values of reserve capacity
by organ system were then calculated within selected
age ranges. Eight separate parameters of reserve
capacity (e.g., nerve conduction velocity, basal meta-
bolic rate, maximal breathing capacity, standard cell
water, standard renal plasma flow, vital capacity,
standard glomerular filtration rate, and cardiac index)
were observed to have declined steadily with chronological age to about 20% by age 80. Reserve capacity
was at approximately 70–80% at age 20 for the same
parameters.
Others researchers have also documented consistent patterns of change in physiological parameters
associated with aging. For example, concentrations
of free testosterone circulating in the serum of
males were shown to decline at a consistent agedependent rate after age 50, leading to a steady rise in
hypogonadism that reaches 50% by age 80 (Harman
et al. 2000). When a more sensitive measure of serum
testosterone is used, the percentage of males experiencing hypogonadism by age 80 climbs to 94%.
Using longitudinal data, it has been demonstrated
that between the ages of 30 and 70, fat-free body
mass for males declined by an average of 3 kg per
decade (Forbes et al. 1970; Flynn et al. 1989; Flynn
et al. 1992). Women were found to have lost fatfree body mass only after age 50, which coincides
with the onset of menopause. Interestingly, the rate
of loss of both muscle and body mass are amenable to
modification through diet and exercise (Fiatarone et al.
40
Table 5. Summary of relative risks and their (P-values) generated from a proportional hazard model used
to compare age patterns of mortality for B6CF1 mice dying of known causes to those where a cause of
death could not be determined (CDU). Relative risks less than one indicate that CDU animals have a lower
age-specific risk of death (i.e., dying at older ages) within the specified time window than mice where a
cause of death could be determined. P-values = (0.00) represent significance values less than (0.001).
Sex
Relative risks (P-value) within quartiles of the failure distribution
1st quartile
2nd quartile
3rd quartile
4th quartile
Quartiles 2–4
F
M
2.21 (0.00)
1.21 (0.26)
0.79 (0.01)
0.70 (0.00)
0.93 (0.75)
0.65 (0.04)
0.48 (0.01)
0.63 (0.02)
0.74 (0.11)
0.79 (0.15)
Table 6. Summary of odds ratios and their (P-values) generated from logistic regression analyses used to contrast deaths
for B6CF1 mice with known causes to those where a cause of death could not be determined (CDU). Odds ratios greater
than one indicate elevated pathologies in CDU animals. P-values = (0.00) represent significance values less than (0.001).
NA means variable not included in final model.
Sex
Cancer
Cardio
Kidur
Lvr
Pul
Repro
Total
F
M
0.11 (0.00)
0.11 (0.00)
0.40 (0.00)
0.39 (0.00)
0.34 (0.00)
0.19 (0.00)
0.19 (0.00)
0.18 (0.00)
0.29 (0.00)
0.33 (0.00)
0.40 (0.00)
NA
3.29 (0.00)
3.76 (0.00)
Cancer: diseases involving cancer.
Cardio: diseases of the circulatory system.
Kidur: diseases of urinary tract.
Lvr: diseases of liver and biliary tract.
Pul: diseases of the respiratory system.
Repro: diseases of the reproductive organs.
Total: total number of pathologies observed within an animal.
1990), but significant age-related declines still appear
to be inevitable. Many other age-related changes in
the physiological functioning of the human body have
been documented, including the loss of maximum
oxygen consumption (Astrand 1960), increase in
systolic blood pressure (Lakatta 1979), loss of total
body water that influences cardiac output (Goldman
1970), loss of lean body mass (Novak 1972), decline
in the mineral content and density of bones (Garn
1975), and many others. Although many of these and
other physiological parameters associated with aging
have been shown to be amenable to partial modification through physical exercise (Bortz 1982), a large
increase in life expectancy is not among the benefits
derived from lifestyle modifications.
Discussion
It has been suggested that there is no demographic
evidence from recent trends in mortality for the existence of limits on the life expectancy of humans, or that
low mortality populations are approaching such limits
if they do exist. It has been further suggested that there
are no biological or demographic reasons why death
rates for humans cannot decline to zero (Wilmoth
2001). If death rates for humans can decline to zero,
then it follows that limits cannot exist for either the life
span of individuals or the life expectancy of populations. In this study, we demonstrated that for mice,
dogs and humans there are verifiable and consistent
age-dependent changes in each species’ reproductive
biology, underlying physiology, and pathology burden
that support the conclusion that the bodies of living
things (including humans) are subject to biological
warranty periods that limit the duration of their lives.
If most humans, on average, are biologically
capable of living to 100 years or more as claimed
(Vaupel 1997), then there should be little evidence of
significant functional decline or pathologic anomaly
among people living to the average survival times
(75–80 years) that are already being attained today.
The same logic should apply to other species as
well. To examine this issue, the life courses of
the mouse, dog and human were first partitioned
into biologically meaningful age windows. Agerelated changes in reproduction, physiological function and the pathology observed at death were then
41
examined in order to determine whether biological
changes consistent with the effects of aging could
be detected within these windows. The goal was to
determine whether this biological evidence was more
consistent with bodies capable of much longer survival
than is currently observed, or with bodies that have
approached or even surpassed (via medical interventions) the expiration date of their biological warranty
periods.
The earliest age window examined was the reproductive period – a period of the life span dominated
by a biology thought to play a major role in why and
when aging occurs (Carnes et al. 1999). The data for
female mice demonstrate that indicators of physiological decline in reproduction (e.g., smaller litter
sizes, lower pup survival, longer intervals between
litters) were detectable at ages that were only 1/3 of the
median age at death for the mouse strains examined.
The reproductive data for human females from a broad
range of fertility and mortality backgrounds demonstrate that some girls as young as 9 years of age have
given birth, and that by 35 years of age approximately
75% of the reproduction that will be accomplished
by females, has been accomplished. Just like female
mice, the reproductive age window for human females
opens and closes at ages that are far younger than
the life expectancy at birth currently achieved by
women in low mortality countries (80 years). In addition, this age pattern of female fertility is remarkably
similar for high mortality, low mortality and natural
fertility populations (see Figure 5). These data suggest
that like female mice (see Figures 1–3), the reproductive biology of human females is well defined and
follows a stable and highly predictable time course. If
evolutionary theories of aging are correct, the reproductive biology of a species is intimately related to the
temporal manifestations of aging and the age distribution of death (Charlesworth 1994; Holliday 1996;
Ellison 2001). The largely immutable reproductive
biology observed for female mice and humans and the
predictable age patterns of their respective mortality
are consistent with bodies that are subject to biological
warranty periods.
Unlike females, human males do not experience
an abrupt cessation of reproductive capacity with
age (Vermeulen 2000). Researchers have looked for
andropause, the male equivalent of menopause, but
have been unable to find it. Instead, there are:
(1) documented cases of 90-year-old men becoming
fathers, (2) data showing that 50% of 80-year-old
men remain fertile, and (3) studies showing that infer-
tility problems among couples rarely involve the male
partner (Schill 2001). Nevertheless, males do experience age-related declines in reproductive capacity
which include reductions in the number of Leydig
(testosterone producing) cells, a parallel decrease in
bio-active testosterone, diminished adrenal androgen
secretion, morphological alterations (thickening and
hernia-like protrusions) of the seminiferous tubules,
increases in structural chromosomal abnormalities in
spermatozoa, and lower libido (Plas et al. 2000). The
greater risk of birth defects (especially heart-related
disorders) associated with older fathers (Lian et al.
1986) – tentatively linked to transcriptional errors
arising from the continuous cell division in spermatogenesis – has led the American Fertility Society to
recommend an age cutoff of 50 years for semen donors
(Bordson et al. 1991). Reproductive data like these
suggest that while most males are biologically capable
of reproducing longer than females, their age patterns
of fertility exhibit a decline remarkably similar to that
observed in females (Figure 5).
The fertility data presented in this paper are for
20th century humans. Since many women in modern
times consciously delay their fertility, it is likely that
the ages associated with specified levels of cumulative fertility for modern women are higher than those
experienced by their ancestors. As such, the median
age at death for humans from intrinsic causes estimated from the mouse model probably err on the
high side (see Table 1). Intrinsic mortality was used
as an endpoint in order to eliminate the contaminating influence of extrinsic causes of death (i.e.,
accidents, homicide, infectious and parasitic diseases,
suicide) that vary so dramatically between populations
(Shryock et al. 1975). If humans adhere to the same
relationship between reproduction and longevity as
mice, then the predicted median age of death from
intrinsic causes would be less than 100 years (see
Table 1). Furthermore, because deaths from extrinsic
causes can never be completely eliminated, a more
realistic estimate of life expectancy for humans as
predicted from the mouse model would be in the range
of 85–95 years. This result is incompatible with the
prediction from extrapolation models that life expectancy for humans will reach or exceed 100 years in the
21st century.
Next, the age window under examination was
expanded to include the post-reproductive period – a
period of the life span that has typically been associated with a loss of functional integrity (Fries 1980).
For a wide range of physiological parameters derived
42
from published studies of humans, approximately 80%
of functional capacity is lost by age 80. Significantly,
this is an age that, when viewed in terms of life
expectancy, has been achieved by only a few populations (i.e., among females in some parts of the world).
Because there is no aging or death program, the agedependent rate of loss of some but not all of this lost
functional capacity can be reduced through exercise,
diet, and with medications. Nevertheless, the biological evidence is clear; the documented degradation
of function (vital capacity) over time for numerous
physiological parameters is consistent with bodies
whose duration of functional existence is subject to
biological warranty periods.
The data on the pathology burdens observed at
death provide incontrovertible evidence that age takes
a severe toll on the bodies of mice, dogs and humans.
Laboratory animals surviving to the 4th quartile of the
failure distribution (operationally defined as old age in
this paper) experienced an increased burden of tumors
that neither caused nor contributed to death, more
pulmonary disease, and more frequent diseases of
the skeleton. Using nothing more than this pathology
profile, it was possible to statistically distinguish
animals that died old from those that died young.
Although death certificate data for humans are far
less reliable than the pathology diagnoses available
for laboratory animals, the pathology implications are
no less conclusive. For humans dying over the age of
80, every organ system exhibits a greater burden of
disease involvement (abnormal pathology) than was
observed in people dying before age 50. As with the
reproductive and physiology data, humans have an
age-related pathology burden that is consistent with
bodies that are subject to biological warranty periods
that limit the duration of life.
Conclusions
The regularity of the rise in human life expectancy
during the 20th century perceived by the advocates
of mathematical extrapolation has led them to predict
that a continuation of this trend into the future will
produce a life expectancy of 100 years by the year
2060. Dramatic reductions in childhood death rates
were responsible for most of the unprecedented life
expectancy gains achieved during the 20th century.
Duplicating these gains in low mortality populations
is not possible because the lives of children can only
be saved once.
The advocates of mathematical extrapolation also
ignore the biomedical significance of the profound
shift that has occurred in the causes of death. Historically, infectious and parasitic diseases (extrinsic
mortality) caused the vast majority of deaths in
humans. Heart disease, cancer, stroke and diabetes
(intrinsic mortality) dominate the mortality schedule
today. Biologically, there is no reason to expect that
these two fundamentally different categories of death
should or would adhere to the same mortality trend.
Contrary to the perception of those advocating
extrapolation methods for projecting life expectancy,
the time frame from the past that has been used to
predict the future is anything but representative of
the historical mortality experience of humans. The
quantum leap in life expectancy achieved over the last
100 years is an unprecedented anomaly in a human
history better characterized by fluctuating (Olshansky
et al. 1996), stagnating, or slowly rising trends in
life expectancy (McNeill 1976). Because the future
course of mortality cannot possibly mimic such an
episodic anomaly (characterized by declining early
age mortality), this unusual time frame should not
be used as the basis for predicting the future course
of human life expectancy. The public policy implications of this recommendation are evident; it is essential
that government agencies responsible for assessing the
future solvency of their age-based programs incorporate biological reasoning into their long-term forecasts.
Death is a biological phenomenon of individuals,
not a mathematical property of populations, and the
biological evidence is undeniable. The pathology
burden within individuals clearly exhibits an age
dependence. Cancer and cardiovascular disease are
symptoms of a complex underlying age-related pathogenesis that causes cells to lose functionality; a functionality that is necessary for the health and well-being
of the individual. The molecular repair processes that
maintain the functional integrity of cells also degrade
over time. Managing the symptoms of age-related
disease (geriatric medicine) is not the same as intervening in the underlying processes (biogerontology)
that give rise to these manifestations (Hayflick 2000;
Carnes et al. 2001). Although evolution does not
and cannot produce genetic programs for aging or
death, forces of deterioration that exist at virtually
all levels of biological organization (e.g., molecules,
cells, tissues, organs) lead to the undeniable conclusion that there is a limit (expiration date) to how long
(warranty period) an individual can live. Since every
43
member of a population is operating under their own
unique warranty period, then it is equally impossible
to deny that limits also exist for the life expectancy of
populations.
Although aging and death are not programmed,
they are nevertheless a predictable byproduct of stable
reproductive biologies that evolved under environments far less conducive to survival than those experienced today. Although it is likely that anticipated
advances in biomedical technology and lifestyle
modification will permit life expectancy to continue its
slow rise over the short-term, a repetition of the large
and rapid gains in life expectancy observed during
the 20th century is extremely unlikely. Such gains
would require an ability to slow the rate of aging
(Miller 2002; de Gray et al. 2001) – a technological
capability that does not exist today, and even if it
did, would require implementation on a broad scale
in order to have a measurable impact on the vital
statistics of a population (Olshansky et al. 2001). As
such, mathematical models that assume the future
course of life expectancy over the long-term will
continue the trend observed during the 20th century
will inevitably fail because they ignore the underlying biology that influences duration of life. Further,
the predictions of extreme longevity (life expectancy
of 100 years or more) produced by these models
are not supported by the biological evidence. Life
expectancy is a statistic derived from a population of
individuals whose biology is the product of an evolutionary history that established the tempo of growth,
development and maturation needed to survive and
reproduce. The image of a biological warranty period
for the duration of life was used to capture a universal
and undeniable biological reality – indefinite survival
is not possible, and the duration of life would remain
limited by biological constraints even if every cause of
premature death could be eliminated.
Acknowledgments
We would like to express our appreciation to Frank
Williamson for his meticulous attention and help on all
matters involving data from Argonne National Laboratory. Similarly, we thank Fletcher Hahn from the
Lovelace Respiratory Research Institute for providing
their dog data and his advice on pathology issues.
We would also like to thank Natalia Gavrilova for
her help in collecting, organizing, analyzing and
plotting the human data. We also would like to
acknowledge the constructive comments made by the
reviewers. Funding for this work was provided by the
National Institute on Aging (Grant Nos. AG00894-01,
AG13698-01, and a supplement to P30 AG12857).
Note
1. Terms like longevity, duration of life and life span are generic
measures of how long an individual exists. Although circumscribed survival is implied, these terms make no distinction
between lives that are cut short by premature death and life span
potentials that are achieved by individuals. Further, these terms
convey no sense of why length of life has or should have limits.
The image of ‘biological warranty periods’ was our attempt
to remedy these shortcomings. A warranty period explicitly
suggests a time frame within which failures are not anticipated. Using ‘biological’ as an adjective restricts the warranty
to biological failures, and implies that failures of biological
origin are likely to occur when survival extends beyond the
warranty period. In this sense, a warranty period for duration
of life is shorthand for the widely accepted view (Olshansky et
al. 2002) that the accumulation of damage to the basic building
blocks of life (DNA, proteins, carbohydrates and fats) eventually exceeds the maintenance and repair capacities of the
body, which then renders the individual vulnerable to forces of
morbidity and mortality. Unlike mechanical devices, biological
warranty periods are an inadvertent byproduct of evolutionary
neglect, and genetic programs for growth, development and
reproduction.
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